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The Rapid Decay of the Optical Emission from GRB 980326 and
its Possible Implications
P.J. Groot 1 , T.J. Galama 1 , P.M. Vreeswijk 1 , R.A.M.J. Wijers 2 , E. Pian 3 , E. Palazzi 3 , J.
van Paradijs 1;4 , C. Kouveliotou 5;6 , J.J.M. in 't Zand 7 , J. Heise 7 , C. Robinson 4;6 N. Tanvir 2 ,
C. Lidman 8 , C. Tinney 9 , M. Keane 10 , M. Briggs 4;6 , K. Hurley 11 , J.­F. Gonzalez 8 , P. Hall 12 ,
M.G. Smith 10 , R. Covarrubias 10 , P. Jonker 1 , J. Casares 13 , F. Frontera 3 , M. Feroci 14 , L.
Piro 3 , E. Costa 3 , R. Smith 15 , B. Jones 16 , D. Windridge 16 , J. Bland­Hawthorn 8 , S.
Veilleux 17 , M. Garcia 18 , W.R. Brown 18 , K.Z. Stanek 18 , A.J. Castro­Tirado 19;20 , J.
Gorosabel 19 , J. Greiner 21 , K. J¨ager 22 , A. B¨ohm 22 , K.J. Fricke 22

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ABSTRACT
We report the discovery of the optical counterpart to GRB 980326. Its rapid
optical decay can be characterized by a power law with exponent --2.10\Sigma0.13 and
a constant underlying source at R c =25.5 \Sigma0.5. Its optical colours 2.1 days after
the burst imply a spectral slope of --0.66\Sigma0.70. The fl­ray spectrum as observed
with BATSE shows that it is among the 4% softest bursts ever recorded. We
1 Astronomical Institute `Anton Pannekoek', University of Amsterdam, & Center for High Energy
Astrophysics, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands
2 Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK
3 CNR Bologna, Via P. Gobetti 101, 40129 Bologna, Italy
4 Physics Department, University of Alabama in Huntsville, Huntsville AL 35899, USA
5 Universities Space Research Association
6 NASA/MSFC, Code ES­84, Huntsville AL 35812, USA
7 Space Research Organisation of the Netherlands (SRON), Sorbonnelaan 2, Utrecht, The Netherlands
8 ESO, Casilla 19001, Santiago 19, Chile
9 Anglo­Australian Observatory, PO Box 296 Epping, NSW 2121, Australia
10 Cerro Tololo Interamerican Observatory, Casilla 603, La Serena, Chile
11 UC Berkeley, Space Sciences Laboratory, Berkeley, CA 94720­7450, USA
12 Department of Astronomy, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 3H8,
Canada
13 Instituto Astrof'isica de Canarias, Tenerife, Spain
14 Istituto di Astrofisica Spaziale, CNR, Via Fosso del Cavaliere, Roma, I­00133, Italy
15 University of Wales, Cardiff, UK
16 University of Bristol, Bristol, UK
17 Department of Astronomy, University of Maryland, College Park, MD 20742, USA
18 Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA
19 Laboratorio de Astrof'isica Espacial y F'isica Fundamental (LAEFF­INTA), P.O. Box 50727, E­28080
Madrid, Spain
20 Instituto de Astrof'isica de Andaluc'ia (IAA­CSIC), P.O. Box 03004, E­18080 Granada, Spain
21 Astrophysikalisches Institut Potsdam, D­14482 Potsdam, Germany
22 Universit¨ats­Sternwarte G¨ottingen, Geismarlandstr. 11, D­37083 G¨ottingen, Germany

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argue that the rapid optical decay may be a reason for the non­detection of
some low­energy afterglows of GRBs.
Subject headings: Gamma­rays bursts---gamma­rays:observations---radiation
mechanisms:non­thermal
1. Introduction
The redshift determinations for GRB 970508 (Metzger et al., 1997) and GRB 971214
(Kulkarni et al., 1998) have demonstrated that GRBs originate at cosmological distances
and are therefore the most powerful photon sources in the Universe, with peak luminosities
exceeding 10 52 erg/s, assuming isotropic emission. Afterglow studies of GRB 970228
(Galama et al., 1997, 1998a), GRB 970508 (Galama et al., 1998b, c, d; Pedersen et al.,
1998; Castro­Tirado et al., 1998a), and GRB 971214 (Halpern et al., 1998, Diercks et al.,
1998) show a generally good agreement with fireball model predictions (Wijers, Rees and
M'eszar'os, 1997; Sari, Piran and Narayan, 1998, hereafter SPN98).
There are, however, a few marked cases where no X­ray or optical afterglow is seen,
most notably GRB 970111 (optical:Castro­Tirado et al., 1997; Gorosabel et al., 1998,
X­rays, debated: Feroci et al.,1998), GRB 970828 (optical: Groot et al., 1998a) and
GRB 980302 (X­rays). In the last case, RXTE/PCA scanning, starting only 1.1 hours
after the burst, found no X­ray afterglow at a level ?1 mCrab. One possible explanation
for the lack of optical counterparts is the extinction by large column densities of gas and
dust, obscuring the GRB afterglows (Groot et al., 1998a; Halpern et al., 1998). This might
indicate an origin in star­forming regions where large quantities of gas and dust are present
(e.g. Paczy'nski, 1998). However, this scenario does not so readily explain the non­detection
of an X­ray afterglow.
GRB 980326 was detected (Celidonio et al., 1998) on Mar. 26.888 UT with one of
the Wide Field Cameras (WFCs; Jager et al., 1997) and the Gamma Ray Burst Monitor
(GRBM; Frontera et al., 1997; Feroci et al., 1997) on board BeppoSAX (Piro, Scarsi and
Butler, 1995), with Ulysses (Hurley et al., 1998) and with the Burst and Transient Source
Experiment (BATSE; Briggs et al., 1998) on board the Compton Gamma Ray Observatory.
Its best WFC position is RA= 08 h 36 m 26 s , Decl = --18 ffi 53: 0 0 (J2000), with an 8 0 (radius)
accuracy. RXTE/PCA scanning 8.5 hours after the burst sets an upper limit of 1.6\Theta10 \Gamma12
erg cm \Gamma2 s \Gamma1 on the 2--10 keV X­ray afterglow of GRB 980326 (Marshall and Takeshima
1998). Time­of­arrival analysis between the Ulysses spacecraft, BeppoSAX and BATSE,
allows the construction of an Interplanetary Network (IPN) annulus which intersects the

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BeppoSAX WFC camera error box (Hurley et al., 1998). The combined WFC/IPN error
box is shown in Fig. 1.
In the BATSE energy range (25--1800 keV) the event lasted ¸ 5s, is resolved into three
narrow peaks, with a peak flux of 8.8\Theta10 \Gamma7 ergs cm \Gamma2 s \Gamma1 , over a 1s timescale. This places
it at the knee of the logN­logP distribution (Meegan et al. 1996). Its total 25--1800 keV
fluence was 1.4\Theta10 \Gamma6 ergs cm \Gamma2 . The event averaged spectrum has a shape typical of GRBs
(photon index \Gamma3:1 +0:25
\Gamma0:5 ), but its E peak , where the šF š spectrum peaks, is unusually low:
E peak =47\Sigma5 keV. Only 4% of the bursts in the sample of Mallozzi et al. (1998, over 1200
GRBs) have smaller E peak values. However, Mallozzi et al. have also shown that there is a
correlation between GRB intensity and spectral hardness (expressed in E peak values). For
bursts with similar peak fluxes, the smallest E peak value there is ¸ 70 keV (Mallozzi, private
communication), which demonstrates the exceptional softness of the integrated spectrum of
GRB 980326.
2. The optical counterpart
Optical Cousins R c ­band observations started at the Anglo­Australian Telescope (AAT)
on Mar. 27.40 UT, followed by observations at the 3.5m New Technology Telescope (NTT)
and the 1.54m Danish telescope (1.5D) at ESO (Chile), the 4m Victor Blanco telescope at
CTIO (Chile), the Fred Lawrence Whipple 1.2m (FLW 1.2m; USA) telescope, the 1.5m
Bologna University (BO; Italy) telescope and the 2.2m Calar­Alto (CAHA 2.2m; Spain)
telescope (see Table 1). All observations were debiased and flatfielded in the standard
fashion. Table 2 shows the magnitude of the comparison stars in all photometric bands
used. Note that star 2 (see Fig. 1) was not detected in the B­band calibration frames.
From a comparison of the first observations at the AAT and ESO/CTIO we discovered
one clearly variable object (Groot et al., 1998b). Its location is RA=08 h 36 m 34: s 28, Dec =
--18 ffi 51 0 23: 00 9 (J2000) with an 0: 00 4 accuracy. Fig. 1 shows the region of the OT. Aperture
photometry on the combined WFC/IPN error box for the first AAT and CTIO epoch
found, apart from asteroid 1998 FO 126 at R c =22.7, no other object with a change in
magnitude ?0.4 mag down to R c =23. Although the variability of sources at R c ? 20 is very
poorly known, we conclude that the optical transient is the counterpart to GRB 980326,
also considering the exhibited power law decay.
Figure 2 shows the R c ­band light curve of the optical transient. It exhibits a temporal
decay which, as applied in previous bursts, can be fitted with a power law and a constant
source: F š / t \Gammaff + C. The power law exponent, ff = 2.10\Sigma0.13, is by far higher than that

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of previous afterglows. The light curve exhibits a flattening, with a fitted constant source
of 25:5 \Sigma 0:5 (ü 2 for the fit is 10.2/9), such as observed for GRB 970508 (Pedersen et al.,
1998; Garcia et al., 1998; Castro­Tirado et al., 1998b), which is possibly the signature of
an underlying host galaxy. Grossan et al. (1998) reported an elongation in the NE­SW
direction, which is also suggested by visual inspection of the NTT observations taken April
1.08 UT, but S/N levels are too low to draw any conclusion. Visual inspection of the
observations reported by Djorgovski et al. (1998) displays an elongation in exactly the
perpendicular direction (SE­NW), which may be an effect of fading of the optical transient.
This would mean that it is not in the center of an underlying galaxy.
On the night of Mar. 29.0 UT broadband BV I c measurements of the optical transient
were made at the NTT (V and I c ) and at CTIO (B). From the fit to the light curve
presented in Fig. 2 we deduce an R c ­band value of 24.50 \Sigma 0.10 at Mar 29.0 UT. The
colours of the transient at this time were B \Gamma R c = 0.53\Sigma0.34, V \Gamma R c ? --0.25, R c \Gamma I c ! 2:1
(3oe limits on V and I c ). The B \Gamma R c value implies an, uncertain, spectral power law index,
F (š) / š \Gammafi , of fi = 0:66\Sigma0.70. One has to realise though, that the underlying source might
contribute significantly to the colours, depending on the difference between the afterglow
and constant source spectrum.
3. Constraints on the electron distribution
Afterglow observations of GRBs over the last year show that a relativistic blast wave,
in which the highly relativistic electrons radiate via the synchrotron mechanism, provides
a generally good description of the observed properties (Wijers, Rees and Mesz'ar'os,1997;
SPN98). Here we will discuss briefly the implications of the power­law decay exponent
ff and the optical spectral slope fi for a number of different blast wave models. For an
extensive discussion on blast wave models and their application to GRB afterglows we refer
the reader to Wijers, Rees and Mesz'ar'os (1997), SPN98 and Galama et al. (1998c).
All models have that the flux F (š; t) / t \Gammaff š \Gammafi for a range of frequencies and times
which contain no spectral breaks. In each model or spectral state of a model ff and fi are
functions only of p, the power law exponent of the electron Lorentz factor (fl e ) distribution,
N(fl e ) / fl \Gammap
e
. The measurement of either one of ff or fi therefore fixes p, and predicts the
other one.
Given the poor constraint on the spectral slope, we cannot uniquely fit GRB 980326, but
we will examine whether its rapid decay requires special circumstances. First we assume that
both the peak frequency šm and the cooling frequency š c (see SPN98 for their definitions)

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have passed the optical passband at 0.5 days. In this case p = (4ff + 2)=3 = 3:5 \Sigma 0:1,
and fi=p/2 = 1.75 \Sigma0.06. The second possibility is when šm has already passed the
optical at 0.5 days, but š c not yet at 4.2 days. In this state p = (4ff + 3)=3 = 3:8 \Sigma 0:1,
and fi = \Gamma(1 \Gamma p)=2 = 1.4 \Sigma0.06. Although the latter case agrees slightly better with
the measured B \Gamma R c spectral slope, we are hesistant to draw any conclusion from this,
considering the uncertainty of the spectral slope. Both, however, imply a much steeper
electron spectrum for this burst than the value p = 2:2 derived for GRB 970508 (Galama
et al. 1998c, d). In case the blast wave is jet­like, the inferred electron spectrum will only
be different if the opening angle, `, of the jet is less than the inverse of the opening angle,
here ! 7 ffi , in which case for slowly cooling electrons p = ff = 2:1, and for rapidly cooling
electrons p = ff \Gamma 1 = 1:1 (Rhoads 1998). In both cases fi = 0:55 \Sigma 0:05, consistent with the
optical colour. Values of p less than 2 are often considered implausible, because they imply
a very efficient acceleration mechanism in which the most energetic electrons carry the bulk
of the energy.
4. The maximum value of p
What is the maximum value of p that can be reached in shock acceleration? In
non­relativistic strong shocks it is generally accepted that p ¸2 (Bell, 1978; Blandford and
Ostriker, 1978). In ultra­relativistic shocks however, the situation is not so clear (Quenby
and Lieu, 1989). Recent calculations show that in this case p will be between 3.2 and 3.8,
depending on the morphology of the magnetic field (Achterberg and Gallant, 1998). This is,
however, when the electrons do not radiate an appreciable part of their energy during shock
acceleration. If the electrons do radiate significantly, as is suggested GRB 970508 (Galama
et al., 1998c,d; SPN98), the electron spectrum will steepen and the distribution of electrons
will no longer be a pure power law. In a power­law model fit, measured values exceeding
p ¸ 3:8 are therefore expected and as a consequence, power law decays of afterglows that
are even more rapid than the ff=2.10 found here are entirely possible.
5. Explanations for non­detections: rapid decays and galactic halos
The optical behaviour of bursts like GRB 970828 (Groot et al., 1998a) and GRB 971214
(Halpern et al., 1998) can be explained by extinction due to gas and dust between the
observer and the origin of the GRB source. However extinction will fail to explain the
non­existence of an X­ray afterglow above 4--5 keV since at these energies extinction is
negligible. The fact that all BeppoSAX NFI follow­ups have detected an X­ray afterglow

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(with the possible exception of GRB 970111, Feroci et al., 1998) and that only two
RXTE/PCA scannings (for GRB 970616 and GRB 970828) have produced X­ray afterglows,
makes the question arise what the cause of this difference is.
Suppose we have an X­ray afterglow that decays as a power law with exponent ff.
What is the X­ray afterglow flux needed shortly (¸ 1 minute) after the burst, as a function
of ff, if we want to detect the afterglow at a level of ¸ 1mCrab after a few hours? The
X­ray flux after 1 minute can be estimated by the X­ray emission detected in the burst
itself, since this X­ray emission will be a mixture of the X­ray tail of the GRB and the start
of the X­ray afterglow. We can therefore derive an estimate of the upper limit to the X­ray
afterglow level after a few hours from the prompt X­ray emission.
Figure 3 shows the flux needed after 1 minute for a detection after 1, 2 and 5 hours at
a level of 1 mCrab as a function of decay rate ff. For bursts that have detected X­ray or
optical afterglows we have also plotted in Fig. 3 the observed total X­ray fluxes during the
bursts versus the X­ray power law decay index ff. (For GRB 980326 we used the optical ff,
since no X­ray afterglow decay index is known.) Because of the mixture explained above
these points actually comprise a set of upper­limits for the flux in the X­ray afterglow after
one minute. It is not only clear from Fig. 3 that most of the bursts that have been found
to exhibit an X­ray afterglow would have been missed by an RXTE/PCA scan after 2--5
hours, but also that this is particularly the case for bursts with high values of ff. A rapid
decay is therefore a viable explanation for the non­detection of bursts, even as bright as
GRB 980203, by the current RXTE/PCA follow­up. It has to be noted that the scanning of
the RXTE/PCA is often performed over no more than the 1.5--2oe BATSE errorboxes, and
there exists therefore a 5--14% chance of not scanning the GRB.
For bursts that show neither X­ray nor optical afterglows, a different explanation may
be found in the fact that all five detected optical afterglows are associated with galaxies.
In the merging neutron­star scenario, a substantial fraction of bursts would occur in a
galactic halo, where the average density of the interstellar medium is ¸1000 times less than
in a disk. Since the afterglow peak flux, Fm , depends on the square root of the density of
the ambient medium, this would mean a reduction of the afterglow peak flux by several
magnitudes with respect to bursts that go off in higher density regions (M'esz'aros and Rees,
1997). Since GRBs are detected by their prompt fl­ray emission, probably produced by
internal shocks (M'esz'aros and Rees, 1997), this would be independent of the density of the
ambient medium.

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6. Conclusions
We have detected the optical counterpart to GRB 980326. Its temporal decay is well
represented by a power law with index --2.10, faster than for any previously found GRB
afterglow, and a constant contribution at R c = 25.5\Sigma 0.5, which is most likely caused
by an underlying galaxy. Fireball models can give an adequate description of this rapid
power law decay of GRB 980326, although its limited optical spectral information makes it
hard to distinguish between different models. This emphasizes the need for multi­colour
photometry, even when the optical counterpart has not yet been found.
A rapid temporal decay may be a reason for the non­detection of low­energy afterglows
of bursts that had X­ray and optical follow­ups. The occurrence of GRBs in galactic
halos, in the merging neutron star scenario, may be an alternative explanation for the
non­detection of low­energy afterglows. To establish the viability of these explanations
for the non­detection of low­energy afterglows, it is of vital importance that more GRB
afterglows are found and this is only possible when low­energy follow­up begins as soon as
possible (!1hr) after the initial GRB event.
Acknowledgments PJG wishes to thank Bram Achterberg for useful discussions.
TJG is supported through a grant from NFRA under contract 781.76.011. RAMJ is
supported by a Royal Society URF grant. CK acknowledges support from NASA grant
NAG 5­2560.
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Fig. 1.--- The combined BeppoSAX WFC and IPN arc error box for GRB 980326, an AAT
Mar. 27.4 UT, 1: 0 6\Theta1: 0 6 R c ­band finding chart of the field of the optical transient and a small
inset of the immediate surroundings of the OT, made from addition of the last three NTT
nights. The solid IPN annulus is the BeppoSAX/Ulysses (S/U) annulus, the dotted annulus
is the BATSE/Ulysses (B/U) annulus. Local comparison stars are indicated by no. 1--4.
S/U
Sax WFC
B/U
­18 o
­18 o
­18 o
­18 o
o
­19
o
­19
46
02
Declination
Right Ascension
*
50
54
58
06
20
40
8:37:00 08:36:00 40
1
4
2
3
OT
OT

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Fig. 2.--- R c ­band light curve of GRB 980326. All errors are 1oe, all upper limits are 3oe. The
dashed line indicates the power law decay and constant source fit (see Sect. 2).
Fig. 3.--- The X­ray flux needed after 1 minute to detect a GRB after 1 (solid line) or 2
(dashed line) and 5 (dashed­dotted line) hrs at a level of 1 mCrab as a function of temporal
decay power law index ff. Indicated for several bursts with measured ff is the total X­ray flux
during the GRB event. References: GRB 970228 Costa et al., 1997; GRB 970402 Nicastro
et al., 1997; GRB 970508 Galama et al., 1998a, Sokolov et al., 1998; GRB 970828 Yoshida
et al., 1998; GRB 971214 Halpern et al., 1998, Diercks et al., 1998; GRB 980326 this paper;
GRB 980329 In 't Zand et al., 1998.

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Table 1: Log of observations of GRB 980326, supplemented with published observations of
the Keck II and KPNO 4­m telescopes.
Date (UT) Telescope Integration time (s) Magnitude OT Reference
Mar. 27.31 Keck II R c =21.19 \Sigma 0.1 GCN #33
Mar. 27.401 AAT 240 R c =21.98 \Sigma 0.16
Mar. 27.437 AAT 240 R c =22.18 \Sigma 0.16
Mar. 27.84 BO 1.5m 3600 R c ?21.85 GCN # 42
Mar. 27.852 CAHA 3300 R c ?22.0
Mar. 28.016 ESO NTT 1200 R c =23.66 \Sigma 0.12
Mar. 28.017 ESO 1.5Dan 2700 R c =23.43 \Sigma 0.25
Mar. 28.045 CTIO 4m 600 R c =23.50 \Sigma 0.12
Mar. 28.120 FLW 1.2m 3600 R c ?22.5
Mar. 28.178 ESO NTT 1200 R c =23.60 \Sigma 0.12
Mar. 28.25 Keck II R c =23.69 \Sigma 0.1 GCN # 32
Mar. 29.09 CTIO 4m 3120 B=25.03\Sigma0.33
Mar. 29.035 ESO NTT 1800 I c ?22.4
Mar. 29.008 ESO NTT 1800 V ?24.2
Mar. 29.424 AAT 480 R c ?23.0
Mar. 30.078 ESO NTT 5400 R c =24:88 +0:32
\Gamma0:26
Mar. 30.2 Keck II R c =25.03 \Sigma 0.15 GCN #35
Mar. 31.082 ESO NTT 5400 R c =25:20 +0:23
\Gamma0:20
Apr. 1.080 ESO NTT 5400 R c ?24.9
Apr. 7.15 KPNO 4m 3300 R c ?24.4
Apr. 17.3 Keck II R c =25.5\Sigma0.5 GCN #57
Table 2: The magnitudes of the four comparison stars used a
Star no. B V R c I c
1 20.05\Sigma0.10 19.17\Sigma0.07 18.51\Sigma0.03 18.11\Sigma0.02
2 ­ 23.04\Sigma0.15 21.85\Sigma0.10 20.74\Sigma0.05
3 21.08\Sigma0.10 20.76\Sigma0.05 20.40\Sigma0.05 20.00\Sigma0.02
4 20.73\Sigma0.10 20.22\Sigma0.05 19.78\Sigma0.03 19.53\Sigma0.02
a Photometric calibration of our observations was performed using Landolt (1992) standard fields
SA98 and Rubin 149 (R c ­band, taken at the AAT at Mar. 27.4 UT), and PG1047+003 (B, V and
I c ­band, taken at ESO at Mar. 30.05 UT).